Open-channel flow (Manning) worksheet with answers

Free printable Open-channel flow (Manning) worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
b = 5 my = 2.2 mn = 0.015

Water flows uniformly 2.2 m deep in a rectangular brickwork channel 5 m wide (Manning n = 0.015). The bed drops 4 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 5 my = 2.2 mn = 0.015drop = 4 m/km
V = m/s
2.Easy
b = 1.5 my = 1.6 mn = 0.012

Water flows uniformly 1.6 m deep in a rectangular finished concrete channel 1.5 m wide (Manning n = 0.012). The bed slope is S = 0.002. Use Manning’s equation in SI units to find the mean velocity V.

b = 1.5 my = 1.6 mn = 0.012S = 0.002
V = m/s
3.Medium
b = 3 my = 2.2 mn = 0.022, S = 0.002

A rectangular clean earth channel is 3 m wide. Water flows uniformly 2.2 m deep. Manning n = 0.022 and the bed slope is S = 0.002. Find the flow rate Q in m³/s.

b = 3 my = 2.2 mn = 0.022S = 0.002
Q = m³/s
4.Medium
b = 5.5 my = 1.4 m1 : 1n = 0.014, S = 0.003

A trapezoidal unfinished concrete channel has a bottom width of 5.5 m and side slopes of 1:1 (horizontal:vertical). Water flows uniformly 1.4 m deep. Manning n = 0.014 and the bed slope is S = 0.003. Find the flow rate Q in m³/s.

b = 5.5 my = 1.4 mz = 1n = 0.014S = 0.003
Q = m³/s
5.Hard
b = 2 my = 0.6 m2 : 1n = 0.025, Q = 2.3 m³/s

A trapezoidal gravel channel with a bottom width of 2 m and side slopes of 2:1 (horizontal:vertical) must carry 2.3 m³/s in uniform flow at a depth of 0.6 m. Manning n = 0.025. Find the required bed slope S (in m/m).

Q = 2.3 m³/sb = 2 my = 0.6 mz = 2n = 0.025
S = m/m
6.Hard
D = 300 mmn = 0.013, V = 0.6 m/s

A concrete sewer with an inside diameter of 300 mm (Manning n = 0.013) must reach a self-cleansing velocity of 0.6 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 300 mmn = 0.013V = 0.6 m/s
S = m/m

Answer key

  1. 1. V = 4.682 m/s
  2. 2. V = 2.381 m/s
  3. 3. Q = 12.43 m³/s
  4. 4. Q = 38.32 m³/s
  5. 5. S = 0.002945 m/m
  6. 6. S = 0.001924 m/m

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